Several RRDO methods [1]}, [2]}, [3]}, [4]} have been reported in recent years. Stochastic design optimization using Monte Carlo (MC) based uncertainty quantification is the most simplified method. It can estimate the probability of failure and the objectives' moments of the system directly, but a large number of simulation points are needed for accurate stochastic responses. It makes the Monte Carlo use in the stochastic design process very time-consuming. Many simulation samples are needed to ensure accuracy, making MC-based robust optimization very time-consuming for implementation when numerical simulations for real-life engineering test cases are involved. Alternatively, a more recent uncertainty quantification methods based on polynomial chaos [5]}, [6]} is used by numerous researchers. For optimization, two kinds of algorithms are usually used: gradient-based and gradient-free genetic algorithms. In polynomial chaos-based robust optimization, the polynomial chaos method is used to estimate the mean and standard deviations of the objective functions at each iteration point of the design process.
